Preservers of matrix pairs with bounded distance

Linear Size Distance Preservers

The famous shortest path tree lemma states that, for any node s in a graph G = (V,E), there is a subgraph on O(n) edges that preserves all distances between node pairs in the set {s}×V . A very basic question in distance sketching research, with applications to other problems in the field, is to categorize when else graphs admit sparse subgraphs that preserve distances between a set P of p node...

On Nonlinear Preservers of Weak Matrix Majorization

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Linear preservers of two-sided matrix majorization

For vectors X, <span style="fon...

Better Distance Preservers and Additive Spanners

Wemake improvements to the current upper bounds on pairwise distance preservers and additive spanners. A distance preserver is a sparse subgraph that exactly preserves all distances in a given pair set P . We show that every undirected unweighted graph has a distance preserver on O(max{n|P |, n|P |}) edges, and we conjecture that O(n|P |+ n) is possible. An additive subset spanner is a sparse s...